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📅 February 27, 2026 👤 scraface

Feb 27, 2026

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🔥 Popular Posts

لذلك، يكون حاصل الضرب قابلاً للقسمة على $8 \cdot 3 = 24$.
نختبر مثالاً: $1 \cdot 2 \cdot 3 \cdot 4 = 24$، والذي ليس قابلاً للقسم...
إذن، أكبر عدد صحيح يجب أن يقسم حاصل ضرب أي أربعة أعداد صحيحة متتالية ه...
السؤال: ما هي أكبر قيمة ممكنة للقاسم المشترك الأكبر $(a,b)$، إذا كان م...
الحل: ليكن $d = \gcd(a, b)$. إذن $a = dx$، $b = dy$، حيث $\gcd(x, y) =...
ثم $a + b = d(x + y) = 96$، لذا يجب أن يكون $d$ قاسمًا للعدد $96$.
لتعظيم $d$، نختار أكبر قاسم للعدد $96$ بحيث يكون $x + y$ عددًا صحيحًا...
أكبر قاسم للعدد $96$ هو $48$، مع $x + y = 2$. الزوج $(x, y) = (1, 1)$...
إذن، $a = 48 \cdot 1 = 48$، $b = 48 \cdot 1 = 48$، و$\gcd(a,b) = 48$.
لذلك، أكبر قيمة ممكنة لـ $\gcd(a,b)$ هي $\boxed{48}$.

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